Path: ...!eternal-september.org!feeder3.eternal-september.org!news.eternal-september.org!.POSTED!not-for-mail
From: "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com>
Newsgroups: sci.math
Subject: Re: Incompleteness of Cantor's enumeration of the rational numbers
Date: Mon, 2 Dec 2024 16:31:21 -0800
Organization: A noiseless patient Spider
Lines: 16
Message-ID: <viljgp$3k21l$13@dont-email.me>
References: <vg7cp8$9jka$1@dont-email.me> <vhv61v$25uqa$5@dont-email.me>
 <b75deca6b1a0631255cf1402ee83db2b266edd22@i2pn2.org>
 <vhvnvc$2aq7k$1@dont-email.me>
 <3fe6ef31f562e0ddf598de46cf864986ca909687@i2pn2.org>
 <vi1pul$2n5v3$1@dont-email.me>
 <9cb8aec671200bb6d71582fd607b876b7ec4c83a@i2pn2.org>
 <vi43br$3cllo$3@dont-email.me> <vi4ak0$3e1nc$1@dont-email.me>
 <vi4b5d$3dq30$1@dont-email.me>
 <40292abc147fee5a7bdd264b69d34ddf2061e59d@i2pn2.org>
 <vi4upt$3hg8t$1@dont-email.me>
 <c43fe07653eac2a9cc0432a6e289bfa1307613f8@i2pn2.org>
 <vi6rau$3v0dn$1@dont-email.me>
 <0bc3cdc8c096bba16decd94ad2af85d35da9b7b4@i2pn2.org>
 <vi7jv2$377e$1@dont-email.me> <9896cb31-806b-40a2-a03e-dc4aea744d04@att.net>
 <298a18e0-a0c6-4db2-901d-da255ecace0b@tha.de>
 <0b2e9a84-f5b3-4f02-8f78-7781da9175af@att.net> <vid55l$1777k$3@dont-email.me>
 <df6328ea-a741-426c-bb1a-4bde16cbfcab@att.net> <vidbob$18gdq$2@dont-email.me>
 <47ccedfd-7c29-4c1a-a411-bbb0c27726e8@att.net> <viiqt8$2qq41$7@dont-email.me>
 <vijhp0$34mp7$3@dont-email.me>
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8; format=flowed
Content-Transfer-Encoding: 8bit
Injection-Date: Tue, 03 Dec 2024 01:31:21 +0100 (CET)
Injection-Info: dont-email.me; posting-host="f777e730b2e8168ebcdb2932c05660c1";
	logging-data="3803189"; mail-complaints-to="abuse@eternal-september.org";	posting-account="U2FsdGVkX1+T6lJrxK+OLiq3PKd4erIIwGVTYRZ1tSI="
User-Agent: Mozilla Thunderbird
Cancel-Lock: sha1:dPrKz5FzlIrL7rdHdrlVfnM3r1I=
In-Reply-To: <vijhp0$34mp7$3@dont-email.me>
Content-Language: en-US
Bytes: 2458

On 12/1/2024 9:49 PM, Moebius wrote:
> Am 02.12.2024 um 00:19 schrieb Chris M. Thomasson:
> 
>> Infinite[ly many] finite sets:   <<<  [!]
>>
>> { { 1 }, { 1, 2 }, { 1, 2, 3 }, { 1, 2, 3, 4 }, ... }
>>
>> ?
> 
> In fact, in axiomatic set theory (due to von Neumann):
> 
>      IN = {{}, {0}, {0, 1}, {0, 1, 2}, ...}
> 
> where 0 = {}, 1 = {0}, 2 = {0, 1}, ... etc. In general: n+1 = {0, ..., n}.

Indeed. Thanks again!